Locally linear manifold model for gap-filling algorithms of hyperspectral imagery: Proposed algorithms and a comparative study

Landsat 7 Enhanced Thematic Mapper Plus (ETM+) Scan Line Corrector (SLC) device, which corrects for the satellite motion, has failed since May 2003 resulting in a loss of about 22% of the data. To improve the reconstruction of Landsat 7 SLC-off images, Locally Linear Manifold (LLM) model is proposed for filling gaps in hyperspectral imagery. In this approach, each spectral band is modeled as a non-linear locally affine manifold that can be learned from the matching bands at different time instances. Moreover, each band is divided into small overlapping spatial patches. In particular, each patch is considered to be a linear combination (approximately on an affine space) of a set of corresponding patches from the same location that are adjacent in time or from the same season of the year. Fill patches are selected from Landsat 5 Thematic Mapper (TM) products of the year 1984 through 2011 which have similar spatial and radiometric resolution as Landsat 7 products. Using this approach, the gap-filling process involves feasible point on the learned manifold to approximate the missing pixels. The proposed LLM framework is compared to some existing single-source (Average and Inverse Distance Weight (IDW)) and multi- source (Local Linear Histogram Matching (LLHM) and Adaptive Window Linear Histogram Matching (AWLHM)) gap-filling methodologies. We analyze the effectiveness of the proposed LLM approach through simulation examples with known ground-truth. It is shown that the LLM-model driven approach outperforms all existing recovery methods considered in this study. The superiority of LLM is illustrated by providing better reconstructed images with higher accuracy even over heterogeneous landscape. Moreover, it is relatively simple to realize algorithmically, and it needs much less computing time when compared to the state- of-the art AWLHM approach.